Problem 105 Determine whether each statement... [FREE SOLUTION]

Chapter 2: Problem 105

Determine whether each statement is true or false. $$ |-8-3|=8-3 $$

Short Answer

Expert verified

False. The statement is not true.

Step by step solution

Simplify the Absolute Value Expression

Calculate the value inside the absolute value brackets: $-8 - 3 = -11$. Now take the absolute value of $-11$: $|-11| = 11$.

Simplify the Expression on the Right Side

Calculate the right-hand side of the equation: $8 - 3 = 5$.

Compare the Two Sides of the Equation

Now compare the two results from previous steps: Left Side: 11 Right Side: 5 Since 11 is not equal to 5, the statement $|-8-3| = 8 - 3$ is false.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Integer Subtraction

Understanding integer subtraction is fundamental in solving equations especially when dealing with numbers having different signs. Let's visualize what happens when you subtract 3 from -8:

The starting point is -8, which is 8 units to the left of zero on a number line.
Subtracting 3 means we take 3 steps further left. So it is like starting at -8, moving to -9, then -10, and finally -11. This gives us -11 as the result of $-8 - 3$.

Subtraction is simply moving leftward on a number line if you are using negative numbers, enhancing clarity when visualizing subtraction operations.

Equation Solving

Solving equations, especially those involving absolute values, requires a sound grasp of how these values operate. An absolute value converts any negative expression inside it into a positive one. Let's look at how this translates into $|-8 - 3| = 8 - 3$:

First, simplify within the absolute value by performing the integer subtraction: $-8 - 3 = -11$.
Next, convert this result to its absolute value: $|-11| = 11$.
Meanwhile, solving $8 - 3$ on the right gives us $5$. So you end up comparing $11$ and $5$.

Practicing these steps helps in mastering equations and understanding the nature of absolute values.

Comparing Values

When it comes to comparing values, especially in equations, accuracy is everything. For instance, analyzing the equation $|-8 - 3| = 8 - 3$ teaches us important lessons in comparing both complex and simple numerical expressions.

The left side simplifies as $11$ due to the absolute value around $-11$.
The right side simplifies as $5$ because it is a straightforward subtraction.
Finally, comparing these results: $11eq5$ confirms that the initial statement does not hold true.

The skill of comparison not only validates equations but also strengthens logical reasoning with numbers.

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91影视

Determine whether each statement is true or false. $$ |-8-3|=8-3 $$

Short Answer

Step by step solution

Simplify the Absolute Value Expression

Simplify the Expression on the Right Side

Compare the Two Sides of the Equation

Key Concepts

Integer Subtraction

Equation Solving

Comparing Values

One App. One Place for Learning.

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